Solvay process is used for preparation of $N a_{2} CO _{3}$.
In this process, precipitate of $NaHCO _{3}$ is obtained,
which is filtered and heated up to obtain $Na _{2} CO _{3}$.
Step I $NH _{3}+ H _{2} O + CO _{2} \rightarrow NH _{4} HCO _{3}$
$CaCO _{3} \xrightarrow{\Delta}CaO + CO _{2}$
Step II $NaCl + NH _{4} HCO _{3} \rightarrow NaHCO _{3}+ NH _{4} Cl$
Step III $2 NaHCO _{3} \stackrel{\Delta}{\rightarrow} Na _{2} CO _{3}+ H _{2} O + CO _{2}$
But in case of potassium, $K HCO _{3}$ is soluble in water so it cannot be precipitated out.
Due to which its decomposition is not possible.
Hence, $K _{2} CO _{3}$ cannot be obtained from this process,